On codes from norm-trace curves
From MaRDI portal
Publication:1400980
DOI10.1016/S1071-5797(03)00010-8zbMath1032.94015MaRDI QIDQ1400980
Publication date: 17 August 2003
Published in: Finite Fields and their Applications (Search for Journal in Brave)
normfootprintGröbner basistracealgebraic geometry codesminimum distanceevaluation codesGoppa boundorder boundhyperbolic codes
Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Applications to coding theory and cryptography of arithmetic geometry (14G50)
Related Items (32)
Bases of Riemann-Roch spaces from Kummer extensions and algebraic geometry codes ⋮ Higher Hamming weights for locally recoverable codes on algebraic curves ⋮ The second weight of generalized Reed-Muller codes in most cases ⋮ On puncturing of codes from norm-trace curves ⋮ On parameters of subfield subcodes of extended norm-trace codes ⋮ On Weierstrass Semigroups of Some Triples on Norm-Trace Curves ⋮ A new family of Castle and Frobenius nonclassical curves ⋮ On the Hermitian curve and its intersections with some conics ⋮ Isometry-Dual Flags of Many-Point AG Codes ⋮ Rational points on cubic surfaces and AG codes from the norm-trace curve ⋮ Generalized Weierstrass semigroups and Riemann-Roch spaces for certain curves with separated variables ⋮ Multi-point codes over Kummer extensions ⋮ Minimal codewords in norm-trace codes ⋮ On Field Size and Success Probability in Network Coding ⋮ On the Geil-Matsumoto bound and the length of AG codes ⋮ On the subfield subcodes of Hermitian codes ⋮ Feng-Rao decoding of primary codes ⋮ Algebraic Geometry Codes from Castle Curves ⋮ Two-Point Codes on Norm-Trace Curves ⋮ Generalized Sudan’s List Decoding for Order Domain Codes ⋮ Evaluation codes from order domain theory ⋮ Intersections between the norm-trace curve and some low degree curves ⋮ On nested code pairs from the Hermitian curve ⋮ Weight distribution of Hermitian codes and matrices rank ⋮ Improved decoding of affine-variety codes ⋮ An improvement of the Feng-Rao bound on minimum distance ⋮ On the second weight of generalized Reed-Muller codes ⋮ On plane curves given by separated polynomials and their automorphisms ⋮ Steane-enlargement of quantum codes from the Hermitian function field ⋮ Quantum codes from one-point codes on norm-trace curves ⋮ An improvement of the Feng-Rao bound for primary codes ⋮ The second generalized Hamming weight of certain Castle codes
Cites Work
- On the structure of order domains
- A fast decoding method of AG codes from Miura-Kamiya curves \(C_{ab}\) up to half the Feng-Rao bound
- Decoding affine variety codes using Gröbner bases
- A note on Hermitian codes over GF(q/sup 2/)
- Footprints or generalized Bezout's theorem
- Improved geometric Goppa codes. I. Basic theory
- On the existence of order functions
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: On codes from norm-trace curves
